Question

x.øi5ized yo-yo is made from two identical solid disks each of mass
M = 2.20 kg and radius R = 9.3 cm. The two disks
are joined by a solid cylinder of radius r = 4.00 cm and
mass m = 1.00 kg as in the figure below. Take the center
of the cylinder as the axis of the system.

(a) What is
the moment of inertia of the system? Give a symbolic answer. (Use
M, R, r, and m as appropriate.)

(b) What torque does gravity exert on the system with respect to
the given axis?
N·m

(c) Take downward as the negative coordinate direction. As depicted
in the figure above, is the torque exerted by the tension positive
or negative?

positivenegative

(d) Is the angular acceleration positive or negative?

positivenegative

(e) What about the translational acceleration?

positivenegative

(f) Write an equation for the angular acceleration α
(alpha) in terms of the translational acceleration a and
radius r. (Watch the sign!)

(g) Write Newton's second law for the system in terms of
m, M, a, T, and g. (Do
this on paper. Your instructor may ask you to turn in this
work.)

(h) Write Newton's second law for rotation in terms of I,
α, T, and r. (Do this on paper. Your
instructor may ask you to turn in this work.)

(i) Eliminate α from the rotational second law with the
expression found in part (f) and find a symbolic expression for the
acceleration a in terms of m, M, g,
r and R. õ >x.øi5 (j) What is the
numeric value for the system's acceleration?
m/s2